Fantastic work. I don’t think you’d be hard-pressed to make Apple Music much worse (hopefully I never apply for an internship there lest they see this), but I really think you’ve done a great job making thoughtful, systemwide improvements.
I think the fact that Apple is trying to add video to a product called Apple Music speaks to the broader problem with their approach. Google has unified all entertainment under “Google Play”, while Apple continues to have confusing and separate brands and systems (iTunes, Apple Music, “Music” app, TV app, etc.) with no clear sense of structure and blurred distinctions. So the problems you identified in the Apple Music iPhone app are really more broadly reflective of the flaws in Apple’s current entertainment offerings as a whole.
Best of luck to you, I’d love to see more case studies in the future! Your interviews added a lot of value and you obviously studied Apple’s design language throughly.